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Maths Puzzle Magazines

Understanding Ratios

Ratios are a concept that is introduced to us in mathematics and sometimes can be difficult to grasp.

What is a ratio?

A ratio is a pair of numbers that make a comparison. Specifically, a ratio compares two numbers using a fraction. They can be written in various ways, for instance:

1 to 3
1:3
1/3

Probably the one that you will see most commonly whilst doing maths in school (at least in England) is the middle one. And sometimes you might get even more than two numbers in the ratio, so you might have 2:3:5 for instance.

The best way to understand a ratio is to think of an example to explain it, and lets go for the old classic, coloured socks!

Imagine I have a drawer that is full of red, yellow and blue socks.

If I know the ratio of red, yellow and blue socks is described by 2:3:5 then I know that for every two red socks there will be three yellow and five blue. So the ratio tells us how to relate things to each other, and specifically what proportion they are in.

How to work out a ratio

Now let's take another classic example - school kids! If there are 18 girls and 12 boys in the class, then you might get asked to turn that into a ratio. No need to panic.

All you do is put the numbers next to each other like this: 18:12 - and that's the ratio of girls to boys!

Now it is good practice to reduce a ratio down as low as you can, and to do that we divide by six on both sides to get a final ratio of 3:2.

Calculating a number from a ratio

Some questions will ask you to go 'the other way round' and request you determine a number based on being told a ratio.

Say for instance you are told that the ratio between girls and boys in a class is 3:2 above. But if you are then told there 60 pupils in the class, not 30, then how do you work out how many boys and girls there are in the class?

Well, you know that for every 3 girls there are 2 boys. So, for every 5 children, there are 3 girls and 2 boys. So now all we need to do is work out - if that's the case for 5 kids - what's the case for 60? We need to work out the multiplication factor. To do that, we see how many times 5 goes into 60 - and the answer is 12.

So we now know all we need to do is multiply 3 x 12 to find the number of girls, and 2 by 12 to work out the number of boys. And so we get there are 36 girls and 24 boys.

As a final tip, when you calculate the numbers from a ratio add them together to make sure you have the correct number! And, indeed, 36 + 24 = 60, and we had 60 children at the start of the calculation, so our answer makes sense!